THE 3 PRIMES THEOREM WITH ALMOST EQUAL SUMMANDS

The problem of representing all sufficiently large odd numbers as the sum of three nearly equal primes is tackled using the Hardy-Littlewood circle method in tandem with a sieve method. A combination of the Bar man and vector sieves: as developed by Baker, Barman and Pintz, is use d. To do this, the major arcs of the circle method involve the investi gation of the mean-values of Dirichlet polynomials, while the minor ar cs demand short-range estimates for exponential sums.